Vol. 29, No. 1, 1969

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Triple series equations involving Laguerre polynomials

John S. Lowndes

Vol. 29 (1969), No. 1, 167–173
Abstract

In this paper it is shown that the problem of solving the triple series equations of the first kind

n=0A nΓ(α + 1 + n)Ln(α;x) = 0, 0 x < a, (1)
n=0A nΓ(α + β + n)Ln(α;x) = f(x), a < x < b, (2)
n=0A nΓ(α + 1 + n)Ln(α;x) = 0, b < x < , (3)
and the triple series equations of the second kind
n=0B nΓ(α + β + n)Ln(α;x) = g(x), 0 x < a, (4)
n=0B nΓ(α + 1 + n)Ln(α;x) = 0, a < x < b, (5)
n=0B nΓ(α + β + n)Ln(α;x) = h(x), b < x < , (6)
where α + β > 0, 0 < β < 1, Ln(α;x) = Lnα(x) is the Laguerre polynomial and f(x), g(x) and h(x) are known functions, can be reduced to that of solving a Fredholm integral equation of the second kind. The analysis is formal and no attempt is made to supply details of rigour.

Mathematical Subject Classification
Primary: 45.20
Secondary: 33.00
Milestones
Received: 2 October 1967
Published: 1 April 1969
Authors
John S. Lowndes